A person sits at the top of a large, smooth hemispherical dome of radius R. Starting from rest, the person slides down along the surface of the dome. (a) Find the speed of the person v as a function of 0. (b) At a moment when the person's speed is some value v, find the normal force acting on the person. (c) Find the angle 0c at which the person loses contact with the dome.
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- an initially stationary block of mass m on a floor. A force of magnitude 0.500mg is then applied at upward angle u=20.What is the magnitude of the acceleration of the block across the floor if the friction coefficients are (a) ms = 0.600 and mk = 0.500 and (b) ms =0.400 and mk = 0.300?In the figure, a block of mass m = 3.71 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F = 12.7 N at an angle 0 = 26.0°. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. What is its value just before the block is lifted (completely) off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted (completely) off the floor? (a) Number i Units (b) Number i Units (c) Number i Units > >Two blocks of masses M1 = 3.5 kg and M2 = 5.7 kg are at rest on a horizontal surface with a coefficient of friction uk = 0.12. You start them moving by pushing on block 1 with a force F1H = 33 N at an angle of 42 degrees below the horizontal. The magnitude of kinetic friction force on each bock is f1 = 6.76 N and f2 = 6.70 N Determine the acceleration of the blocks and the magnitude of the normal force between the blocks.
- A stacked pair of books with masses m1= 2.0 kg (bottom book) and m2 = 1.5 kg (top book) are tossed onto a table. The books strike the table with no vertical velocity and their common horizontal speed is ?o = 0.75 m/s. The kinetic friction coefficient between the bottom book and the table is ?k1=0.45; the kinetic and static friction coefficients between the two books are ?k2=0.3 and ?s2= 0.4. Find the final horizontal position of each book relative to the spot where the stack hits the table.Tarzan, who weighs 777 N, swings from a cliff at the end of a 16.5 m vine that hangs from a high tree limb and initially makes an angle of 21.9° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 721 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?A particle, which remains at rest, is acted on by three forces F, G and H. The force F has magnitude 55 N and is directed to the left and up making an angle of 45 degrees with the vertical The force G is directed vertically down and H is directed to the right and up making an angle of 60 degrees with the vertical. Find the magnitude of the vectors G and H, giving your answers to one decimal place. The magnitude of G is N (to 1 d.p.) The magnitude of H is N (to 1 d.p.)
- A child is playing on a hill with a cardboard box. The combined mass of child and box is ? = 120 kg. He climbs into box, which is initially at rest, at the top of the hill. The hill is inclined at an angle of 30 degrees with respect to the horizontal. The coefficients of static and kinetic friction between the box and the hill are mu s = 0.4 and mu k = 0.2. Consider that the box (with child inside) has begun to slide down the hill (you can assume that it has been given a brief push to get it started moving). What is the magnitude of the acceleration of the box? b. If the hill is 4 m tall, what is the child’s speed when he reaches the bottom? c. At the bottom of the hill, the ground becomes level (horizontal), but the coefficients of friction do not change. How far does the child slide before he comes to a stop? Thank you in advance, it's a lengthy question and I really need help :)In the figure, a block of mass m = 5.44 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F = 10.6 N at an angle 0 = 24.0°. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. What is its value just before the block is lifted (completely) off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted (completely) off the floor? (a) Number Units (b) Number Units (c) Number UnitsA small object is initially at rest at the top of a large solid sphere that is fixed on the ground. The small object then begins to slide along the surface of the large solid sphere, without friction. V₁ = 0 RI Part (a) Find the angle at which the small object loses contact with the large solid sphere. Part (b) Find the maximum horizontal distance traveled by the small object before it hits the ground. Take (xi, y₁) = (0,2R) as the coordinates for the top of the large solid sphere.
- A chandelier hangs h = 0.74 m down from two chains of equal length. The chains are separated from one another by a length L = 0.85 m at the ceiling. The chandelier has a mass of m = 28 kg. What is the angle, θ in degrees, between one of the chains and the vertical where it contacts the chandelier?In the figure, a block of mass m = 3.40 kg is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F = 11.9 N at an angle θ = 29.0°. (a) What is the magnitude of the block's acceleration? (b) The force magnitude F is slowly increased. What is its value just before the block is lifted (completely) off the floor? (c) What is the magnitude of the block's acceleration just before it is lifted (completely) off the floor?A woman pushes a 10.0 kg box across a horizontal floor with a constant force of magnitude 40.0 N directed at an angle of -25° with respect to the positive x-axis. The box moves horizontally to the right. At the origin (x=0) the box has an initial speed of 4.00 m/s and the woman pushes it to a location ofx=3.00 m. what is the force of the woman? what is the force of gravity? what is the normal force of the floor?